If the line passing through $(4, 3)$ and $(2, k)$ is perpendicular to the line $y = 2x + 3$,then the value of $k$ is:

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.

If a line $L$ passing through a point $A(2, 3)$ intersects another line $4x - 3y - 19 = 0$ at the point $B$ such that $AB = 4$,then the angle made by the line $L$ with the positive $X$-axis in the anti-clockwise direction is

Find the value of $x$ for which the points $(x, -1), (2, 1),$ and $(4, 5)$ are collinear.

$A$ line passing through the point $A(2, 3)$ makes an angle of $45^{\circ}$ with the $x$-axis and intersects the line $x + y + 1 = 0$ at point $P$. Find the distance $AP$.

The equation of the hour hand at $4$ o'clock is